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binary Relation Operators

Updated March 28, 2011

Binary relation operators are symbols that establish a relationship between two quantities, usually those before and after the operator. Binary operators seldom have attributes such as subscripts or superscripts.

Standard Binary Symbols

Latex Symbol Description
\in element of, sideways cup with horizontal bar, opening right
\ni contains as member, reverse of \in
\leq less or equal, represented by < over = signs
\geq greater or equal, represented by > over = signs
\ll much less, represented by 2 < in a row
\gg much greater, represented by two > in a row
\prec precedes, < with both lines curving outward
\succ succeeds, reverse of \prec
\preceq precedes or equals, \prec with bottom line repeated below symbol
\succeq succeeds or equals, reverse of \preceq
\sim similar, looks like ~
\cong congruent, a \sim over =
\simeq asymptotically equal, \sym over single horizontal bar
\approx approximately equal, vertical stack of two \sym symbols
\equiv equivalent, represented by a stack of three horizontal bars
\doteq = with a dot above it
\subset subset of, horizontal cup with opening right
\supset superset of, horizontal cup with opening left
\subseteq subset of or equals, \subset over single horizontal bar
\supseteq superset of or equals, reverse of \subseteq symbol
\sqsubseteq squared subset of or equals
\sqsupseteq squared superset of or equals
\smile smile without any surrounding circle
\frown frown, without any surrounding circle
\perp perpendicular symbol, vertical bar above and touching horizontal bar
\models Models, represented by short vertical bar touching short = sign
\mid middle, represented by vertical |
\parallel parallel, represented by two vertical bars in a row
\vdash short vertical bar touching a single short horizontal bar
\Vdash Forces, short double vertical bar touching a single short horizontal bar
\vDash Same symbol as \models
\dashv reverse \vdash
\propto proportional
\asymp asymptotic  smile on top of and touching frown
\bowtie normal subgroup of, bow tie shape or right -pointing triangle on left touching left-pointing triangle on right
\sqsubset square subset of, squared \subset
\sqsupset square superset of, squared version of \supset 
\Join same symbol as \bowtie
\pm ± plus or minus
\mp minus or plus
\times × times multiplication sign
\cdot · dot multiplication symbol
\circ ring operator
\bigcirc large circle
\div ÷ divide, represented by dots above and below horizontal bar
\diamond diamond operator
\ast asterisk operator
\star white star
\cap cap, intersection
\cup cup, union
\sqcap square cap, intersection
\sqcup square cup, union
\wedge wedge, logical AND
\vee V operator, logical OR
\triangleleft left pointing triangle
\triangleright Right pointing triangle
\bigtriangleup wide up triangle
\bigtriangledown wide down triangle
\oplus circled plus
\ominus circled minus
\otimes circled times sign
\oslash circled slash
\odot circled dot operator
\bullet bullet
\dagger daggar
\ddagger double daggar
\setminus \ ∖ Set Minus
\uplus multiset union
\wr wreath product
\amalg ⨿ Amalgamation or Co-product
\lhd Normal subgroup of
\rhd Contains as normal subgroup
\unlhd Normal subgroup of or equals to
\unrhd Contains as normal subgoup or equal to
\dotplus dot plus
\centerdot centered dot
\ltimes Left normal factor semi-direct product
\rtimes Right normal factor semi-direct product
\leftthreetimes Left semi-direct product
\rightthreetimes Right semi-direct product
\circleddash circled minus
\smallsetminus Same as \setminus
\barwedge NAND
\curlywedge curly logical AND
\curlyvee curly logical OR
\veebar XOR
\intercal intercalate
\Cup double union
\Cap double intersection
\circledast circled asterisk operator
\circledcirc circled ring operator
\boxminus squared minus
\boxtimes squared times
\boxdot squared dot operator
\boxplus squared plus
\divideontimes division times
\And & AND

Advanced AMS Binary Symbols

\leqslant less than or slanted equals to
\geqslant greater than or slanted equals
\eqslantless slanted equal to or less than
\eqslantgtr slanted equal to or greater than
\lesssim less or quivalent
\gtrsim greater or quivalent
\lessapprox less than or approximate
\gtrapprox greater or approximate
\approxeq approximately equal
\lessdot less with dot
\gtrdot greater with dot
\lll very much less
\ggg very much greater than
\lessgtr less or greater
\gtrless greater or less than
\lesseqgtr less than equals to or greater than
\gtreqless Greater than equal to or less than
\lesseqqgtr less than above equals to above greater than
\gtreqqless greater than above equals to above less than
\doteqdot geometrically equal
\eqcirc equals with circle in middle
\circeq circled equals
\fallingdotseq Approximately equal to or the image of
\risingdotseq Image of or approximately equal to
\triangleq delta equals
\backsim reverse similar symbol
\thicksim same as \sim (similar) symbol
\backsimeq reverse similar or equals
\thickapprox thick approximately equal
\preccurlyeq precedes or equals
\succcurlyeq succeeds or equals
\curlyeqprec equal or precedes
\curlyeqsucc equal or succeeds
\precsim precedes or equivalent
\succsim succeeds or equivalent
\precapprox precedes above almost equals to
\succapprox succeeds above almost equals to
\subseteqq subset of above equals
\supseteqq superset of above equals
\Subset double subset
\Supset double superset
\vartriangleleft normal subgroup of
\vartriangleright contains as normal subgroup of
\trianglelefteq normal subgroup of or equal
\trianglerighteq contains as normal subgroup or equal
\VDash double vertical bar double right turnstile
\Vdash Forces symbol
\Vvdash Triple vertical bar, right turnstile
\Bumpeq geometrically equivalent
\between between
\pitchfork pitchfork
\backepsilon ϶ reverse Greek epsilon symbol
\blacktriangleleft black small left-pointing triangle
\blacktriangleright black small right-pointing triangle
\therefore therefore
\because because

AMS binary symbols negated

\ne not equal
\notin not an element of
\nless not less
\ngtr not greater
\nleq neither less or equal
\ngeq neither greater or equal
\lneq less than and single line not equal to
\gneq greater than and single line not equal to
\lneqq Less than but not equal to
\gneqq greater but not equal
\lnsim less but not equivalent
\gnsim greater but not equivalent to
\lnapprox less and not approximately equal
\gnapprox greater and not approximately equal to
\nprec does not precede
\nsucc does not succeeds
\npreceq  does not precede or equal
\nsucceq does not succeed or equal
\precneqq Precedes above not equal
\succneqq succeeds above not equal to
\precnsim precedes but not equivalent to
\succnsim succeeds but not equivalent
\precnapprox precedes above not almost equal to
\succnapprox succeeds above not approximately equal to
\nsim not similar
\ncong not congruent
\nmid not divide
\nparallel not parallel
\nvdash does not prove
\nvDash not true
\nVdash not force
\nVDash negated double vertical bar double right turnstile
\ntriangleleft not normal subgroup of
\ntriangleright does not contain as normal subgroup
\ntrianglelefteq not normal subgoup of or equal
\ntrianglerighteq does not contain as normal subgroup or equal
\nsubseteq neither subset of nor equal
\nsupseteq neither superset of nor equal
\subsetneq subset of with not equal
\supsetneq superset with not equal
\subsetneqq subset of above not equal to
\supsetneqq superset of above not equal to

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